To give a sense of what I am looking for ... this is a the circuit's logic diagram of a 4-bit binary to decimal encoder. enter image description here

Here is its truthtable enter image description here

Now, What is the circuit's logic diagram of a 2-bit binary to decimal encoder?

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    \$\begingroup\$ You have the truth table right there in front of you. Draw some Karnaugh maps and you will have the answer. What exactly is causing you difficulty with this problem? \$\endgroup\$ – Elliot Alderson Jul 2 '19 at 19:12
  • \$\begingroup\$ I do disagree. We generally don't like to just give out answers; we prefer to help you learn how to get the answers yourself...otherwise we get into an endless loop of answering the same kind of question over and over again. Maybe you should tell us what you do know. Do you know anything about Boolean algebra? How to read a truth table, how to get minterms or a sum-of-products representation from a truthtable? \$\endgroup\$ – Elliot Alderson Jul 2 '19 at 19:28
  • \$\begingroup\$ I won't draw you the schematic but this should help: Q0 = (NOT A) AND (NOT B) Q1 = A AND (NOT B) Q2 = (NOT A) AND B Q3 = A AND B \$\endgroup\$ – Stiddily Jul 2 '19 at 19:30
  • \$\begingroup\$ Okay, it actually wasn't hard at all. Thank you for the help @Stiddily. Can someone please confirm I did it right? gyazo.com/de33900114d50c7ce8ea1c2423da0cdf \$\endgroup\$ – Sebastian Nielsen Jul 2 '19 at 19:40
  • \$\begingroup\$ Looks right to me @Sebastian Nielsen. I would definitely advise looking into karnaugh maps as well though. They start off fairly simple and will definitely be necessary once you start building bigger things. \$\endgroup\$ – Stiddily Jul 2 '19 at 20:00

it depends which 2 bits you choose out of 4 because you can only get 4 out of 10 decimal equivalent single outputs.

  • for a simple reduction from schematic:

  • with a pencil or your mind, tick off all the first 4 outputs back to the wired inputs and delete the rest not used.

  • it should only require 2 inputs as given in your question
  • or easier trace the 1st two bit inputs A,B to the 4 essential outputs 2^2=4 leaving C,D=0

Since the NAND gates are redundant and two inversions cancel we get.

enter image description here enter image description here

|improve this answer|||||
  • \$\begingroup\$ Can you explain what you mean by "tick off"? I think I know, but beginners might not. \$\endgroup\$ – Elliot Alderson Jul 2 '19 at 20:11
  • \$\begingroup\$ That still seems rather complicated, the easiest would be to just build it from scratch. \$\endgroup\$ – Sebastian Nielsen Jul 2 '19 at 20:15
  • \$\begingroup\$ Ok . Then use an eraser with an image editor or start from scratch , whatever is quicker \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jul 2 '19 at 20:16
  • \$\begingroup\$ I assumed you wanted a quick reduction method from an existing larger scaled solution. This saves time, but you need to learn the fundamentals AND,OR,XOR,NOT with a truth table \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jul 2 '19 at 20:23

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